Question

1/15 for blue, 1/20 for purple, 1/10 for white, and 1/5 for black. What is the probability of pulling a blue or purple card, written as a reduced fraction?

Answer 1

The probability of pulling a blue or purple card is found by adding the probability of pulling a blue card (1/15) and the probability of pulling a purple card (1/20), which results in a combined probability of 7/60 after converting to a common denominator.

Step-by-step explanation:

To calculate the probability of pulling either a blue or a purple card, we simply add their individual probabilities together because the events are mutually exclusive (you can't pull a card that is both blue and purple at the same time).

The probability of pulling a blue card is given as 1/15, and the probability of pulling a purple card is 1/20. Adding these together:

P(blue or purple) = P(blue) + P(purple)= 1/15 + 1/20

To add these fractions, they must have a common denominator. The least common multiple of 15 and 20 is 60, so we convert the fractions to have the denominator 60:

1/15 = 4/60 (by multiplying both the numerator and denominator by 4)
1/20 = 3/60 (by multiplying both the numerator and denominator by 3)

Now we can add them together:

4/60 + 3/60 = 7/60

So, the probability of pulling a blue or purple card is 7/60. This is already in its simplest form, as there are no common factors between 7 and 60.